Question

if p-q√3 = 2-√3/2+√3, then find the value of p and q​

Answer 1

Answer :

• p = 7
• q = 4

Explanation :

Given,

$\longrightarrow \rm \: p - q \sqrt{3} = \dfrac{2 - \sqrt{3} }{2 + \sqrt{3} }$

Find the value of ‘a’ and ‘b’.

Taking R. H. S.

$= \dfrac{2 - \sqrt{3} }{2 + \sqrt{3} }$

Rationalising the denominator,

$\longrightarrow \: \dfrac{2 - \sqrt{3} }{2 + \sqrt{3} } \times \dfrac{2 - \sqrt{3} }{2 - \sqrt{3} }$

$\longrightarrow \: \dfrac{4 - 2 \sqrt{3} - 2 \sqrt{3} + 3 }{ {(2)}^{2} - {( \sqrt{3 }) }^{2} } \{ \because \rm (a - b)(a + b) = a^{2} - b^{2} \}$

$\longrightarrow \: \dfrac{7 - 4 \sqrt{3} }{4 - 3}$

$\longrightarrow \blue{ \dfrac{7 - 4 \sqrt{3} }{1} }$

On comparing with L. H. S.

$\rm \implies \: {7 - 4 \sqrt{3} } = p - q \sqrt{3} \\ \rm \therefore \:p = 7 \: and \: q = 4$

$\Huge{\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_}$

Identity used :

• (a - b) (a + b) = a² - b²